• 제목/요약/키워드: H-function

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Shannon의 함수

  • 이범준
    • 한국해양학회지
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    • 제14권1호
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    • pp.32-38
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    • 1979
  • 생태학에서의 다양성(diversity) 문제는 일반적으로 통용되고 있는 다양성=안정성 (diversity=stability)의 개념과 연관되어 항상 생태학자들의 관심대상이 되어 있다. (Watt 1966). 처음으로 군집(community)의 diversity에 대한 개념을 시도한 것은 Gleason(1922)이며 diversity index의 측정은 Fisher(1943)로부터 시작한다.(in Travers 1979, Hurlbert 1971, Gallucci 1973).

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FOURIER TRANSFORM OF ANISOTROPIC MIXED-NORM HARDY SPACES WITH APPLICATIONS TO HARDY-LITTLEWOOD INEQUALITIES

  • Liu, Jun;Lu, Yaqian;Zhang, Mingdong
    • 대한수학회지
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    • 제59권5호
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    • pp.927-944
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    • 2022
  • Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝn in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.

SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION

  • Baek, In-Soo
    • 대한수학회논문집
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    • 제30권1호
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    • pp.7-21
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    • 2015
  • We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

ON FINITE SUMMATION FORMULAE FOR THE H-FUNCTION OF TWO VARIABLES

  • Gupta, K.C.;Garg, O.P.
    • Kyungpook Mathematical Journal
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    • 제18권2호
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    • pp.211-215
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    • 1978
  • In the present paper, we obtain two new and interesting finite summation formulae for the H-function of two variables in a very neat and elegant form. The novel feature of the paper is that the method used here in deriving these formulae is simple and direct and does not impose heavy restrictions on the parameters involved. On account of the most general nature of the H-function of two variables, a number of related finite summation formulae for a number of other useful functions can also be obtained as special cases of our results. As an illustration, we have obtained here from our main results, the corresponding finite summation formulae for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function. Appell's function and Gauss' hypergeometric function which are also believed to be new.

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Numerical Calculation of the Relaxation Spectrum from the Correlation Function$^\dag$

  • Lee, Hoo-Sung
    • Bulletin of the Korean Chemical Society
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    • 제8권5호
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    • pp.406-408
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    • 1987
  • It has been shown that the distribution of relaxation times, H(ln $\tau$), in semi-logarithmic time scale can easily be calculated numerically from the derivative of the relaxation function in semilogarithmic scale. In that, ln$\tau$, the abscissa, is divided into N different segments of equal size, then H is considered to be a linear function of ln $\tau$within each segment. The technique has been applied to a Williams-Watts function as well as to the relaxation function obtained by photon correlation spectroscopy from atactic polystyrene glass. It has been demonstrated that the relaxation functions can be precisely reproduced from the calculated distribution functions.

적응제어를 위한 $H_{\infty}$ 강인제어기의 설계-다항식 접근방법 (A Study on the $H_{\infty}$ Robust Controller for Adaptive Control-polynomial approach)

  • 박승규
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1996년도 하계학술대회 논문집 B
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    • pp.936-938
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    • 1996
  • The $H_{\infty}$ robust controller is designed for on-line adaptive control application by using polynomial approach. The $H_{\infty}$ robust controllers for adaptive system were designed first by Grimble. But they have a problem that two minimum costs can exist and did not minimize the conventional $H_{\infty}$ cost function which is the $H_{\infty}$ sum of weighted sensitivity and complementary sensitivity terms. In this paper, the two minimum costs problem can be avoided and the conventional $H_{\infty}$ cost function is minimized by employing the Youla parameterization and polynomial approach at the same time. In addition pole placement is possible without any relation with weighting function.

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Effect of Insamyangyoung-tang on the Skin Barrier Function of Hairless Mice

  • Nam, Hae-Jeong;Kim, Yoon-Bum
    • 대한한의학회지
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    • 제28권4호
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    • pp.18-26
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    • 2007
  • Objective : To study the effect of the Insamyangyoung-tang(ISYT) extract on the skin barrier function, the skin pH, skin humidity and transepidermal water loss(TEWL) were measured and histological changes were observed in DNCB(2,4-dinitrochloro-benzen)-induced contact dermatitis(CD) hairless mice. Methods : The male hairless mice were divided into three groups. Each group consisted of 15 mice. The normal group which had acetone- olive oil applied. The control group which had intentionally induced CD by DNCB and it was fed normal saline orally. The ISYT group which had intentionally induced CD by DNCB and it was fed ISYT extract orally for 7 days. The three groups were checked 24h, 48h and 72h later after inducing CD, and the skin pH, skin humidity and TEWL were observed. Tissue samples were taken, and damage to the epithelial cell was observed. Statistical analysis was performed by using one way-ANOVA: significance was set at p values less than 5% (p<0.05). Results : ISYTextract efficiently maintained the pH balance, it kept the skin humidity at a normal level, and it inhibited TEWL of the DNCB-induced CD hairless mouse. The damage to the epithelium was decreased and the regeneration power of the skin was increased in the ISYT group. Conclusion : Insamyangyoung-tang has a good effect on the skin barrier function of DNCB induced contact dermatitis hairless mice.

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Rice blast susceptible mutants of Taebaegbyeo and genes differentially expressed in he wild type rice.

  • Lee, C. H.;C. U. Han;K. S. Jang;Park, Y. H.;H. K. Lim;Kim, J.C.;Park, G. J.;J.S. Cha;Park, J. E.
    • 한국식물병리학회:학술대회논문집
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    • 한국식물병리학회 2003년도 정기총회 및 추계학술발표회
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    • pp.67.2-68
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    • 2003
  • A rice cultivar, Taebaegbyeo, is highly resistant to rice blast and moderately resistant to bacterial leaf blight (BLB) caused by Magnaporthe grisea and Xanthomonas oryzae pv. oryzae, respectively. To study the rice disease resistance mechanism, we generated rice deletion M3 mutants by gamma-ray irradiation. Blast and BLB responses of 16,000 M3 mutants were screened by inoculating mixtures of 4 races (KJ-201, H-1113a, KI-313, KI-409) of M. grisea and 3 Korean races of X. oryzae pv. oryzae. We selected so far 21 M3 mutants of Taebaegbyeo showing high susceptibility to the diseases. One of the mutants, KCT-6417, was susceptible to KI-1113a race of M. grisea, suggesting the deletion of a race-specific blast resistance gene in the mutant. To isolate rice genes involved in blast resistance and defense response, we take a PCR-based suppression subtractive hybridization approach using cDNAs of blast-inoculated wild type and the KCT-6417 as a tester and a driver, respectively. Genes specifically expressed in the wild type will be presented. The selected genes would give us a clue to understand mechanism for the race specific resistance and defense responses against M. grisea H-1113a in Taebaegbyeo.

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ON THE FAILURE OF GORENSTEINESS FOR THE SEQUENCE (1, 125, 95, 77, 70, 77, 95, 125, 1)

  • Ahn, Jeaman
    • 충청수학회지
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    • 제28권4호
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    • pp.537-543
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    • 2015
  • In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.